1. Field of the Invention
The invention relates to automatic feedback control of thermal processing. In particular, the invention pertains to model-based predictive temperature control of thermal process reactors such as used in semiconductor processing.
2. Description of the Related Art
Until recently, most of the high temperature processing necessary for integrated circuit fabrication was performed in hot-wall, resistance-heated batch reactors. Controlling the wafer temperature uniformity (within-wafer, point-to-point) in these reactors was generally not considered an issue, because the reactors were substantially isothermal. The down-boat (wafer-to-wafer) temperature uniformity could be controlled effectively by dividing the cylindrical heating coil into several zones, each with its own temperature sensor controller and power supply. The outer zones were typically adjusted to compensate for heat losses at the furnace ends. Independent, single-loop, off-the-shelf PID controllers suffice for these purposes. The trend to larger wafer diameters, the demanding uniformity requirements for ULSI applications, and the demands for reduced thermal budget all led to an increased use of single-wafer process reactors. For commercially feasible throughput, it is highly desirable to minimize the process cycle time by heating substantially only the wafer and its immediate environment. In many cases, single-wafer reactors are of the cold-wall or warm-wall type, in which quartz or stainless steel process chambers are water or air cooled. Under such circumstances, the system is no longer isothermal and temperature uniformity control becomes an issue of considerable concern and technical difficulty. A recent technical review of the field is provided in xe2x80x9cRapid Thermal Processing Systems: A Review with Emphasis on Temperature Control,xe2x80x9d F. Roozeboom, N. Parekh, J. Voc. Sci. Technol. B 8(6), 1249-1259, 1990.
Specific physical process characteristics serve to exemplify the need for precise temperature uniformity. Homo-epitaxial deposition of silicon should be performed in a manner which minimizes crystalline growth defects, such as lattice slip. Such defects are induced by thermal gradients in the wafer during high temperature processing, becoming more sensitive to gradients as temperature increases. For example, while gradients of about 100xc2x0 C. across an 8-inch wafer may be tolerable at a process temperature of 900xc2x0 C., respective gradients of only 2-3xc2x0 C. are allowable at process temperatures of 1100xc2x0 C. There is some experimental evidence to indicate that gradients of approximately 10xc2x0 C. may be tolerable for a few seconds. The deposition of polycrystalline silicon (polysilicon) typically takes place at 600-700xc2x0 C. where as a rule of thumb a 2% uniformity degradation is incurred for every degree of temperature gradient. Moreover, in heterodeposition processes such as polysilicon deposition, multiple reflections and optical interference within the deposited overlayers can give rise to emissive or absorptive changes with overlayer thickness, exacerbating the problem of maintaining temperature uniformity (J. C. Liao, T. I. Kamins, xe2x80x9cPower Absorption During Polysilicon Deposition in a Lamp-Heated CVD Reactor, J. Appld. Phys., 67(8), 3848-3852 (1990)). Furthermore, patterned layers can also lead to variations in light absorption across the wafer, creating local temperature gradients. (P. Vandenabeele, K. Maex, xe2x80x9cTemperature Non-Uniformities During Rapid Thermal Processing of Patterned Wafers,xe2x80x9d Rapid Thermal Processing SPIE, Vol. 1189, pp. 84-103, 1989).
The aforementioned factors complicating the control system design are not only manifest for rapid thermal chemical vapor deposition (RTCVD) systems, but apply to thermal processing (TP) systems in general, where the need for precise process control is balanced by the demand for minimal process cycle times. The generally short process cycle times and fast dynamics of the single-wafer systems render dynamic control of temperature uniformity a necessity of considerable technical difficulty. The radiant heating systems used for rapid wafer heating comprise either arc lamps or banks of linear tungsten-halogen lamps divided into several independently-controllable heating zones. The wafer itself, in principle, represents a complex thermal system whose interaction with the radiant energy is inherently nonlinear. Furthermore, since the requirements for power distribution over the wafer are different for dynamic compared to steady-state uniformity, it does not suffice to deduce the required power settings from a wafer temperature measurement at a single point. In general, multiple sensors are required to measure and maintain a uniform temperature distribution over the wafer. These considerations render temperature control an essentially multi-input, multi-output (MIMO) or multivariable problem. Due to the large interaction between zones inherently present in radially heated systems, the conventional control techniques, for example, using single-loop, coupled or master-slave type PID control, cannot be expected to provide thermal process reactor systems with the required control specifications for all operating conditions. Conventional PID control techniques are susceptible to lag, overshoot and instability at the desirable process rates, and therefore become limiting factors in single-wafer process reactors. Thus, there is a clear need in electronic materials processing for systems which can maintain precise, dynamic multivariant control while providing commercially viable wafer throughput.
The foregoing discussion has clearly outlined the need for effective uniformity control in thermal process reactors using a multivariable approach. This view is endorsed by many authors. See, for instance, several contributions in the Rapid Thermal and Integrated Processing Symposium, ed. J. C. Gelpey, et al., Mater. Res. Soc. Symp. Proc., Vol. 224, 1991. In particular, articles by Moslehi et al. (pp. 143-156), Apte, et al. (pp. 209-214), and Norman et al. (pp. 177-183), discuss various aspects of multivariable temperature control. Several attempts to develop models for RTP and RTCVD systems are reported in the literature. Two examples, Norman and Gyurcsik, et al., developed different models, both using a first-principles approach, and applied the models to uniformity optimization (S. A. Norman, xe2x80x9cOptimization of Wafer Temperature Uniformity in Rapid Thermal Processing Systems,xe2x80x9d0 ISL Tech. Rep. No. 91-SAN-1, Subm. to IEEE Trous. on Electron Devices, 1991; R. S. Gyurcsik, T. J. Riley, R. Y. Sorrel, xe2x80x9cA Model for Rapid Thermal Processing: Achieving Uniformity Through Lamp Control,xe2x80x9d IEEE Trans. on Semicon. Manf., Vol. 4(1), 1991). The model of Norman (1991) consists of two components. The first component models the (two-dimensional) heat balance of the wafer and is used to compute the steady-state wafer temperature profile for a given heat flux from the lamps. The second component models the heat flux from the lamps as a function of the individual lamp powers. A least-squares method is used to fit a quadratic relationship between the desired temperature at discrete radial positions on the wafer and the flux density due to the lamps. Next, the lamp model is used to determine optimal relative power settings for the lamps that approximate the required flux. This method only applies to the uniformity control in steady-state, i.e., constant input. However, Norman, et al. (1991), consider not only the steady-state optimization problem, but also the problem of designing an optimal trajectory. For this purpose the dynamic model is a finite-difference approximation to the one-dimensional heat equation, including the effects of conduction in the wafer, convective heat loss from the wafer, and radiative transfer. A minimax solution is chosen for the steady-state uniformity optimization and trajectory following.
Dynamic system modeling is an essential ingredient of predictive control laws, which provide the fundamental structure for a unique class of contemporary control algorithms. In essence, system or plant control strategies are based on predicted future plant behavior predicated on a suitably accurate dynamic plant model. The future control strategies are not static and do not extend arbitrarily to future time slots; but rather are periodically updated in accordance with the plant model in a so-called receding horizon fashion. For a number of years, predictive control has been the subject of extensive research and development. Indeed, predictive control is the central theme behind the benchmark works of Cutler and Ramaker in their Dynamic Matrix Control (DMC) algorithm (C. Cutler, B. L. Ramaker, xe2x80x9cDynamic Matrix Controlxe2x80x94A Computer Control Algorithm,xe2x80x9d Joint Automatic Controls Conference Proceedings, San Francisco, 1980) and Richalet, et al., in their Model Algorithmic Control (MAC) algorithm (J. A. Richalet, A. Rault, J. D. Testud, J. Papon, xe2x80x9cModel Predictive Heuristic Control: Application to Industrial Processes,xe2x80x9d Automatica, Vol. 14, No. 413, 1978). Further predictive and adaptive characteristics are incorporated by R. M. C. de Keyser, et al., xe2x80x9cSelf-Tuning Predictive Control,xe2x80x9d Journal A, Vol. 22, No. 4, pp. 167-174, 1981; and more recently by Clarke, et al., in their Generalized Predictive Control (GPC) algorithm (D. W. Clarke, C. Mohtadi, P. S. Tuffs, xe2x80x9cGeneralized Predictive Control. Part I: The Basic Algorithm,xe2x80x9d Automatica, Vol. 23, No. 2, pp. 137-148, 1987). Much of the contemporary control work in the literature is to some extent based on these approaches.
In DMC and other similar approaches, plant models are identified and cast in the form of deterministic impulse-response or step-response models. While these model forms are well-understood, they are often computationally cumbersome and present significant compromises between accuracy and response for long-range model predictions. Further, DMC appears to be incapable of handling non-minimum phase and open-loop unstable plants. A significant redeeming feature of DMC is that of the receding horizon, after which control increments are assumed to be zero. This advantageous assumption is incorporated in GPC, which in various derivations also utilizes extensions of Auto-Regressive Moving Average (ARMA) plant models such as CARMA or CARIMA (Controlled Auto-Regressive Moving Average, CAR-Integrated-MA). The ARMA plant models are generally represented by expressions involving polynomials A, B and C of the time-shift operator qxe2x88x921. The shift operator qxe2x88x921 acts on a function of a discrete time variable f(t), such that qxe2x88x921f(t)=f(txe2x88x921) and in general qxe2x88x92uf(t)=f(txe2x88x92u). The model polynomials A, B and C act on process inputs u(t), process outputs y(t) and process disturbances e(t) such that:
A(qxe2x88x921)y(t)=B(qxe2x88x921)u(t)+C(qxe2x88x921)e(t)
Such models represent both the plant dynamics via the polynomials A,B and the disturbance via A,C. A particular advantage is that the number of parameters in the model is minimal so that they can be estimated with high efficiency. As outlined by Clarke, et al., the long-range plant predictions are best accomplished by recursion of an associated Diophantine equation involving the model parameters. A similar ARMA model and recursive model prediction is also found in U.S. Pat. No. 5,301,101 by MacArthur, et al., which discloses an adaptive receding horizon-based controller incorporating means for operating cost minimization.
Nevertheless, in spite of the recent effort to develop new, useful multivariant control techniques, until now there has been little success in applying them to the demanding conditions imposed by commercial thermal process reactors. The only apparent successes to date has involved the use of physical models rather than the black box models employed herein (see e.g. Cole Porter et. al., xe2x80x9cImproving Furnaces with Model-Based Temperature Controlxe2x80x9d, Solid State Technology November 1996, page 119).
It is an object of the present invention to provide a method and apparatus for a more effective temperature control system in multivariant thermal processes.
In accordance with one aspect of the present invention, a temperature controlled thermal process reactor comprises a chamber within which a thermal process is executed, a source of thermal energy, a thermal sensor, and a model-based predictive temperature controller. One preferred embodiment of the temperature controlled thermal process (TP) reactor comprises a multivariable temperature controlling arrangement. The temperature controller preferably comprises a multivariable thermal process model that relates multivariable process input thermal energy to multivariable process output temperature. The temperature controller also preferably comprises a prediction calculator that uses the process model to calculate a predicted temperature output over a predetermined future time period or prediction horizon. The preferred temperature controller additionally comprises a control calculator that uses the predicted temperature output to calculate an optimum control strategy by which to control the source of thermal energy. The control calculator preferably calculates an optimum future control strategy by comparing the predicted process output variables to a set of desired future process output variables.
In accordance with another aspect of the present invention, a temperature control system for controlling a thermal process comprises a controllable source of thermal energy, a temperature sensor, and a model-based predictive temperature controller. The model-based predictive temperature controller comprises a thermal process model that relates process input thermal energy to process output temperature and a prediction calculator that uses the thermal process model to calculate a predicted nominal temperature output over a predetermined future time period. The temperature controller further comprises a control calculator that uses the predicted nominal temperature output to calculate an optimum strategy by which to control the source of thermal energy. Preferably, the control calculator compares the predicted temperature output to the desired temperature output to derive the optimum control strategy. In a preferred temperature control system, the prediction calculator periodically updates the predictions in accordance with an auto-regressive moving average calculator. In a preferred arrangement, predictions are executed over a predetermined future time period, which is updated in accordance with the auto-regressive moving average.
In still another aspect of the present invention, a method of controlling a thermal process comprises the steps of measuring a process output temperature and using this information in predicting a future process output temperature. The method further comprises calculating an optimum process input control strategy and controlling a process input thermal energy using the calculated optimum process input control strategy. In a preferred embodiment of the method, predicting a future process output temperature comprises identifying a thermal process model relating process input thermal energy to process output temperature. The preferred method of prediction further comprises recursive application of the thermal process model over a predetermined future time period, or prediction horizon. The predictions are furthermore periodically updated in accordance with an auto-regressive moving average calculator. Another preferred method of rapid thermal process control comprises calculating an optimum process input control strategy by comparing the predicted future process output temperature to a desired future process output temperature.
In accordance with another aspect of the present invention, a temperature control system for controlling a thermal process comprises a controllable source of thermal energy, a temperature sensor, and a nonlinear, model-based predictive temperature controller. The model-based predictive temperature controller comprises a nonlinear thermal process model that relates process input thermal energy to process output temperature and a prediction calculator that uses the thermal process model to calculate a predicted nominal temperature output over a predetermined future time period. The nonlinear model further comprises a neural network. In a particularly preferred embodiment, the neural network cmprises hidden neurons that are of the sigmoid type.
In accordance with yet another aspect of the present invention, a temperature control system for controlling a thermal process comprises a controllable source of thermal energy, a temperature sensor, a model-based predictive temperature controller, and a softsensor model that relates susceptor temperatures to wafer temperatures. The softsensor model provides an estimate of the unmeasurable wafer surface temperatures. In a preferred embodiment, the softsensor model is an FIR model. The model coefficients for the softsensor FIR filter are obtained through the use of an instrumented wafer.
In accordance with yet another aspect of the present invention, a temperature control system for controlling a thermal process comprises a controllable source of thermal energy, a temperature sensor, a model-based predictive temperature controller, a softsensor model that relates susceptor temperatures to wafer temperatures and a setpoint generator that uses the output of the softsensor model, and the recipe to adjust the setpoints so that the wafer surface temperatures will be closer to the values specified in the recipe.
The model-based predictive temperature controller comprises a nonlinear thermal process model that relates process input thermal energy to process output temperature and a prediction calculator that uses the thermal process model to calculate a predicted nominal temperature output over a predetermined future time period. The nonlinear model further comprises a neural network. In a particularly preferred embodiment, the neural network cmprises hidden neurons that are of the sigmoid type.